We propose a novel hierarchical, nonlinear model that predicts brain activity in area V1 evoked by natural images. In the study reported here brain activity was measured by means of functional magnetic resonance imaging (fMRI), a noninvasive technique that provides an indirect measure of neural activity pooled over a small volume (~ 2mm cube) of brain tissue. Our model, which we call the SpAM V1 model, is based on the reasonable assumption that fMRI measurements reflect the (possibly nonlinearly) pooled, rectified output of a large population of simple and complex cells in V1. It has a hierarchical filtering stage that consists of three layers: model simple cells, model complex cells, and a third layer in which the complex cells are linearly pooled (called “pooled-complex” cells). The pooling stage then obtains the measured fMRI signals as a sparse additive model (SpAM) in which a sparse nonparametric (nonlinear) combination of model complex cell and model pooled-complex cell outputs are summed. Our results show that the SpAM V1 model predicts fMRI responses evoked by natural images better than a benchmark model that only provides linear pooling of model complex cells. Furthermore, the spatial receptive fields, frequency tuning and orientation tuning curves of the SpAM V1 model estimated for each voxel appears to be consistent with the known properties of V1, and with previous analyses of this data set. A visualization procedure applied to the SpAM V1 model shows that most of the nonlinear pooling consists of simple compressive or saturating nonlinearities.

We describe the Berkeley wavelet transform (BWT), a two-dimensional triadic wavelet transform. The BWT comprises four pairs of mother wavelets at four orientations. Within each pair, one wavelet has odd symmetry, and the other has even symmetry. By translation and scaling of the whole set (plus a single constant term), the wavelets form a complete, orthonormal basis in two dimensions. The BWT shares many characteristics with the receptive fields of neurons in mammalian primary visual cortex (V1). Like these receptive fields, BWT wavelets are localized in space, tuned in spatial frequency and orientation, and form a set that is approximately scale invariant. The wavelets also have spatial frequency and orientation bandwidths that are comparable with biological values. Although the classical Gabor wavelet model is a more accurate description of the receptive fields of individual V1 neurons, the BWT has some interesting advantages. It is a complete, orthonormal basis and is therefore inexpensive to compute, manipulate, and invert. These properties make the BWT useful in situations where computational power or experimental data are limited, such as estimation of the spatiotemporal receptive fields of neurons.